Problem: Solve for $x$ and $y$ using elimination. ${-2x+5y = -1}$ ${6x+4y = 22}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $3$ ${-6x+15y = -3}$ $6x+4y = 22$ Add the top and bottom equations together. $19y = 19$ $\dfrac{19y}{{19}} = \dfrac{19}{{19}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {-2x+5y = -1}\thinspace$ to find $x$ ${-2x + 5}{(1)}{= -1}$ $-2x+5 = -1$ $-2x+5{-5} = -1{-5}$ $-2x = -6$ $\dfrac{-2x}{{-2}} = \dfrac{-6}{{-2}}$ ${x = 3}$ You can also plug ${y = 1}$ into $\thinspace {6x+4y = 22}\thinspace$ and get the same answer for $x$ : ${6x + 4}{(1)}{= 22}$ ${x = 3}$